Problem B. 4774. (February 2016)
B. 4774. The parabolas \(\displaystyle p_1\) \(\displaystyle \big(y=-x^2+b_1 x+c_1\big)\) and \(\displaystyle p_2\) \(\displaystyle \big(y=-x^2+b_2 x+c_2\big)\) are tangent to the parabola \(\displaystyle p_3\) \(\displaystyle \big(y=x^2+b_3x+c_3\big)\). Prove that the line connecting the points of tangency is parallel to the common tangent of \(\displaystyle p_1\) and \(\displaystyle p_2\).
Kvant
(5 pont)
Deadline expired on March 10, 2016.
Statistics:
65 students sent a solution. 5 points: 54 students. 4 points: 3 students. 3 points: 3 students. 1 point: 4 students. Unfair, not evaluated: 1 solutions.
Problems in Mathematics of KöMaL, February 2016